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tmua.me Extreme Set C Paper 1 · Q15

Paper 1Algebra

A cubic polynomial ff satisfies

f(0)=0,f(1)=1,f′(0)f′(1)=4.f(0)=0,\qquad f(1)=1,\qquad f'(0)f'(1)=4.

It is also given that f′(x)≥0f'(x)\geq0 whenever 0≤x≤10\leq x\leq1.

What is the greatest possible value of f(1/2)f(1/2)?

A18\dfrac18
B12\dfrac12
C58\dfrac58
D78\dfrac78
E11
FThere is no greatest value.

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